METHOD FOR CALCULATING THE FIR FILTER BASED ON GENETIC ALGORITHM

Abstract

The paper considers the analysis of the genetic algorithm with the aim of its application to optimize the coefficients of FIR filters with a linear phase. FIR filters are more preferable for some tasks, because they have the following advantages: the group delay of the filter is continual; FIR filters are always stable. A genetic algorithm is a heuristic method, which is a variation of evolutionary algorithms. It solves optimization problems using natural evolution methods similar to natural selection in real world. When solving a problem with a genetic algorithm, the phenotype was identified that determines the real object. As a chromosome, which stores a list of genes (real filter coefficients), a class implemented in the Python programming language is used. As a fitness function, the standard deviation between the approximating and approximated functions of the amplitude-frequency characteristics of the FIR filter (filter with finite impulse response) is used. FIR filter design includes both optimization of filter coefficients and consideration of quantization effects, which can also be implemented using a genetic algorithm. Modeling was carried out on the example of a FIR filter of the first type using the Python programming language. The simulation results showed the effectiveness of the genetic algorithm for the synthesis of FIR filters (the results are comparable with the least squares method). This method can be successfully used in the design of FIR filters with a linear phase in the creation of technical means. It should be noted that the efficiency of the genetic algorithm depends on the generated initial population, as well as on the setting of hyperparameters, therefore, further analysis involves the study of the formation of the initial population, as well as optimization of the hyperparameters of the genetic algorithm.